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prioq.ml
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(*
Copyright (c) 2007-2008 The Regents of the University of California
Copyright (c) 2011 Luca de Alfaro
All rights reserved.
Authors: Luca de Alfaro
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
1. Redistributions of source code must retain the above copyright notice,
this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright notice,
this list of conditions and the following disclaimer in the documentation
and/or other materials provided with the distribution.
3. The names of the contributors may not be used to endorse or promote
products derived from this software without specific prior written
permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
POSSIBILITY OF SUCH DAMAGE.
*)
TYPE_CONV_PATH "UCSC_WIKI_RESEARCH"
(** Priority Queue *)
module Make (A : sig type t val compare : t -> t -> int end) =
struct
exception Empty
type 'a elt = {
mutable priority:A.t;
mutable contents:'a
}
type 'a t = {
mutable n: int; (* number of elements in the queue *)
mutable a:'a elt option array; (* array used to store the queue *)
}
(* returns whether x is smaller than y. *)
let lt x y =
match (x, y) with
| (None, None) -> false
| (Some(x), None) -> true
| (None, Some(x)) -> false
| (Some(x), Some(y)) -> A.compare x.priority y.priority = -1
let create () = { n = 0; a = Array.create 256 None }
let clear q =
for i = 0 to q.n - 1 do
q.a.(i) <- None
done;
q.n <- 0
let is_empty q = q.n = 0
let length q = q.n
let iter (f:int -> A.t -> 'a -> unit) q =
for i = 0 to q.n - 1 do
match q.a.(i) with
| Some(x) -> f i x.priority x.contents
| None -> raise (Invalid_argument "malformed queue")
done
(* priorites are sorted in ascending order *)
let array_swap q i j =
let t = q.a.(i) in
q.a.(i) <- q.a.(j);
q.a.(j) <- t
let child_0 i = i * 2 + 1
let child_1 i = i * 2 + 2
let parent i = (i - 1) / 2
(* percolate_down percolates the element at position i down
towards the root of the funnel, if required.
Smaller elements percolate down. *)
let rec percolate_down q i =
if i > 0 && (lt q.a.(i) q.a.(parent i)) then
begin
array_swap q i (parent i);
percolate_down q (parent i)
end
(** Internal *)
(* This function is used when the root is removed
(from the bottom of the funnel).
The element needs to percolate up the funnel,
each time swapping with the smallest of the two
children, until it is smaller than both children. *)
let rec percolate_up q i =
let swap_and_percolate j =
begin
array_swap q i j;
percolate_up q j
end
in
let i0 = child_0 i in
let i1 = child_1 i in
if i1 < q.n then begin
(* If there is a child_1, then there is also a child_0. *)
if (lt q.a.(i0) q.a.(i)) or (lt q.a.(i1) q.a.(i)) then begin
(* We need to do a swap. *)
if lt q.a.(i0) q.a.(i1)
then swap_and_percolate i0
else swap_and_percolate i1
end
end else begin
(* no child_1 *)
if i0 < q.n then begin
(* there is a child_0, but no child_1 *)
if lt q.a.(i0) q.a.(i) then swap_and_percolate i0
end
end
let add q x p =
let n = q.n in
if n = Array.length q.a then
(* We double the length of the array each time. *)
q.a <- Array.append q.a (Array.create n None);
let c = { priority = p; contents = x } in
q.a.(n) <- Some c;
q.n <- n + 1;
percolate_down q n;
c
let take q =
if q.n = 0 then raise Empty
else
let r = q.a.(0) in
let n = q.n in
q.a.(0) <- None;
q.n <- n - 1;
if n > 1
then
begin
array_swap q 0 (n - 1);
percolate_up q 0
end;
match r with
| Some(x) -> x
| None -> raise (Invalid_argument "malformed queue")
end;;
(* Unit tests *)
module type E =
sig
type t = int
val compare: t -> t -> int
end
module M: E = struct
type t = int
let compare = compare
end
module P = Make (M)
if false then begin
let heap = P.create() in
ignore (P.add heap 3 3);
ignore (P.add heap 4 4);
ignore (P.add heap 5 5);
ignore (P.add heap 1 1);
ignore (P.add heap 2 2);
ignore (P.add heap 7 7);
while (not (P.is_empty heap)) do begin
let m = P.take heap in
let i = m.P.contents in
Printf.printf "Taken: %d\n" i
end done
end